Efficient Vertex-Label Distance Oracles for Planar Graphs

@article{Mozes2017EfficientVD,
  title={Efficient Vertex-Label Distance Oracles for Planar Graphs},
  author={S. Mozes and Eyal E. Skop},
  journal={Theory of Computing Systems},
  year={2017},
  volume={62},
  pages={419-440}
}
We consider distance queries in vertex-labeled planar graphs. For any fixed 0 < πœ– ≀ 1/2 we show how to preprocess a directed planar graph with vertex labels and arc lengths into a data structure that answers queries of the following form. Given a vertex u and a label Ξ» return a (1 + πœ–)-approximation of the distance from u to its closest vertex with label Ξ». For a directed planar graph with n vertices, such that the ratio of the largest to smallest arc length is bounded by N, the preprocessing… Expand
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